Two-layer Reservoir Research Articles

Pore Pressure Diffusion Waves Transmission in Oil Reservoir

Recent studies on seismic wave excitation have revealed that mesoscopic wave-induced fluid flow (WIFF) is a process that attenuates the compressional (P) waves in reservoir rocks at seismic frequency bands. Fluid flow and Biot's slow diffusion (pressure) waves are produced when the P-waves create fluid-pressure gradients at mesoscopic-scale heterogeneities. Pore pressure continuity can be sustained by converting seismic energy into diffusion waves that diffuse away from the interfaces or boundaries. Biot’s diffusion waves fail to comply with a square-law approach because of their slow propagation velocity and higher attenuation. It is currently uncertain how to characterize reservoir fluids in mature oil reservoirs during seismic wave-based enhanced oil recovery (EOR). A simplified 1D two-layer reservoir model was investigated in this study. The findings demonstrate that diffusion wave propagation in oil reservoirs is frequency-dependent and affected by rock permeability and fluid viscosity. At a formation layer interface, it was discovered that diffusion waves obeyed the accumulation-depletion relationship rather than the reflection-refraction approach. Therefore, pore pressure diffusion waves can characterize reservoir fluid during seismic EOR and monitor the CO2 front in depleted reservoirs during storage for CCUS projects. It can also detect shale gas transport in low permeability layers and identify the propagation of fractures during gas/oil recovery.

Dual-phase flow in two-layer porous media: a radial composite Laplace domain approximation

The main purpose of this work is to present an interpretation method for injectivity test in a two-layer reservoir that can be extended to a multilayer approach, based on new analytical solutions to the well pressure response. The developed formulation uses a radially composite reservoir approach and considers that the water front propagation may be approximated by a piston-like flow displacement. The reservoir is assumed to be laterally infinite and properties such as permeability and porosity may be different in each layer. The solutions were developed in the Laplace domain and then inverted to real domain using the Stehfest Algorithm. The proposed formulation was then validated by comparison with a numerical flow simulator. Results showed a good agreement between the numerical simulator and the analytical model. Also, a sensitivity study was done by comparing the results of different scenarios varying oil viscosities and injection flow rate to assess how these properties affect the pressure and pressure derivative profiles.

Investigation on the pressure response behavior of two-layer vertical mixed boundary reservoir: field cases in Western Sichuan XC gas field, China

Pressure response behavior of two-layered reservoir with a vertical mixed boundary is easy to be mistaken for that of the radial composite reservoir or dual-pore reservoir. It is difficult to fit the pressure response curve and easy to obtain abnormal parameter values using a misunderstood model. In this paper, we present the interpretation of three different types of pressure responses of vertical mixed boundary reservoir by our proposed models, where the diagnostic window and feature value are captured for different mixed boundary types. Results show that the mixed boundary with closed boundary and infinite-acting boundary induces the fake pressure response of a radial composite reservoir with poor permeability outer zone. The mixed boundary with the main constant-pressure and non-main closed boundary produces a fake pressure response of a dual-porosity reservoir. The diagnostic window of pressure response curves shape can easily capture the mixed boundary type, and the feature value of the feature values of pressure response value can quickly obtain the permeability ration of one layer. Aiming at different representative types of pressure response cases in the western Sichuan XC gas field, China, we innovatively analyze them from a different perspective and get a new understanding of pressure response behavior of vertical mixed boundary, which provides a guideline for the interpretation of layered oil and gas reservoir with the complex boundary in the vertical direction.

On the possibility of operational management of reservoir pressure in a multilayer reservoir exploited by dual completion and injection method based on recording current gas factor of products extracted from each reservoir

The paper discusses the problem of operating complex and expensive telemetering equipment designed to monitor and control a multilayer field operation using the dual completion and injection method. The author offers an alternative to the applied wireless and wired data transmission (as the first type does not have the required range and the second does not have the required reliability) technology. It is a new method for monitoring and controlling reservoir pressure in real time based on recording the current gas factor of the products extracted from each layer using dual completion method and ensuring its relative stability due to the operational management of their reservoir pressure through the dual injection system. At the same time, it is proposed to use commercially available automated group measure unit equipped with corresponding sensors as the means of measuring gas/oil ratio. Testing the method of reservoir pressure management proposed by the author for the two-layer reservoir of the Tedinskoye field of Lukoil-Severneftegaz confirmed its effectiveness, which served as the basis for the development of an appropriate methodological guide and filing of a patent.

Pressure transient behavior of layered commingled reservoir with vertical inhomogeneous closed boundary

The multilayered deposition is the main feature of the tidal flat reservoir in the western Sichuan Basin. The boundary distance among layers of the tidal flat reservoir is different. To understand the influence of vertical inhomogeneous closed boundary (VICB) on pressure transient behavior, an extended n-layer VICB reservoir model is presented.Firstly, the VICB is discretized into n boundary segments representing the characteristics of the individual layer, and the reservoir is divided into n horizontal layers accordingly. The pressure transient model of the n-layer VICB reservoir is established by the seepage equations and boundary conditions of the individual layer. Secondly, solving Bessel equations consisting of 2n boundary conditions by the Cramer's rule to obtain the bottom-hole pressure solution in Laplace space. The wellbore storage and skin effect are taken into account by Duhamel's principle in the Laplace domain. Lastly, the bottom-hole pressure solution in the real-time domain is obtained by the Stehfest numerical inversion algorithm. The comparison result with the bottom-hole pressure of the two-layer reservoir proves the reliability of the n-layer VICB reservoir model.In the n-layer VICB reservoir model, a new VICB radial flow regime is identified which easily mistaken as the outer radial flow of the composite reservoir model. The result of sensitivity analysis shows that the pressure transient behavior of the n-layer VICB reservoir has the “equivalent compound zone effect” and “equivalent boundary radii effect”. There is a quantitative relation between the distribution of VICB and the characteristics value of pressure derivative during the VICB radial flow regime stage.The “equivalent compound zone effect”, “equivalent boundary radii effect” and the quantitative relation provide a simple and fast analytical method for identifying the vertical distribution and distance range of VICB. Finally, a field case from the western Sichuan Basin multilayered gas reservoir is discussed in detail to validate the capabilities of our model.

Разработка методики фильтрационных исследований на двухслойной модели пласта, моделирующей сложнопостроенный карбонатный коллектор

Разработка методики фильтрационных исследований на двухслойной модели пласта, моделирующей сложнопостроенный карбонатный коллектор

New solution to the pressure transient equation in a two-layer reservoir with crossflow

This paper presents a new mathematical model and an analytical solution to the pressure transient equation of a uniform-flux which fully penetrates the vertical well in a two-layer petroleum reservoir with crossflow. This new model and solution provide an accurate and fast tool to (1) evaluate a vertical well performance in a two-layer reservoir; (2) estimate the effects of formation properties on pressure behavior at the locations both far away from and around the well. The solution is obtained from the model by using Laplace transform, double Fourier transform, and Green’s functions method. When all the corresponding parameters are identical in each layer, the proposed solution for a two-layer reservoir is naturally reduced to the solution for a single layer reservoir. Based on the analytical solution, the pressure of the vertical well, which produces with a constant rate in the two-layer reservoir, can be examined in detail. More importantly, a dimensionless crossflow coefficient is proposed to describe the crossflow in a two-layer reservoir quantitatively. It is verified that the crossflow coefficient is not constant, but a function of the time and distance away from the wellbore. In the numerical experiments, the pressure response is observed in three stages: (1) the first one is similar to the commingled system because the crossflow is very weak at the beginning of the production; (2) the second one is the transition stage when the crossflow becomes stronger with the production; (3) the third stage is close to the performance of the homogeneous system when the crossflow coefficient approaches zero.

Selective withdrawal from an intake channel connected to a reservoir

This paper investigates selective withdrawal from an intake channel connected to a two-layer stratified reservoir using a line sink located at the downstream end of the intake channel. Such a withdrawal scenario is commonly observed at intake channels, skimming operations, and pump intake bays. This study formulates mathematical expressions for such a withdrawal scenario in order to extend our knowledge and to develop a mathematically simpler method in the case where a solution already exists. An expression to compute the incipient Froude number was developed considering the effect of a boundary. Expressions were developed to obtain discharge ratios for the scenarios when the line sink is located at the channel bottom and far away from the channel bottom. When the interface is located below the channel bottom and only at the reservoir, the intake channel itself behaves as a rectangular orifice, and an expression to compute the incipient Froude number for such a case was developed. The mathematical results were compared to the results obtained from a computational fluid dynamics solver and other relevant published studies.

Perforation Sequence Optimization of Fault Block Oil Reservoir with Edge Water on the Basis of Pseudo-filtration Resistance Analysis

Perforation sequence of multiple zone is affected by many factors for natural water flooding in Fault block oil reservoir. In order to study on the affecting factors including permeability, length of banded oil layer and viscosity of oil, a two-layer reservoir model was established. The combination schemes was found for three affecting factors. The numerical simulation research was carried out and influence of the factors on perforation sequence of fault block oil reservoir with edge water was analyzed. The results show that the larger the factor contrast is, the greater the reservoir heterogeneity is, the later the perforation sequence is for the reservoir which has finer property, the more the increased range of recovery ratio is. The boundaries of technique for optimization of multiple zone perforation sequence was determined by the pseudo-filtration resistance ratio with the range between 0.023 and 43.88; The relation graph of pseudo-filtration resistance ratio, pseudo-filtration resistance with optimal perforation sequence was made by Watson interpolation algorithm. It is of great significance to improve the reservoir development effect.

Transient Coupled Borehole/Formation Fluid-Flow Model for Interpretation of Oil/Water Production Logs

Summary Interpretation of two-phase production logs (PLs) traditionally constructs borehole fluid-flow models decoupled from the physics of reservoir rocks. However, quantifying formation dynamic petrophysical properties from PLs requires simultaneous modeling of both borehole and formation fluid-flow phenomena. This paper develops a novel transient borehole/formation fluid-flow model that allows quantification of the effect of formation petrophysical properties on measurements acquired with production-logging tools (PLTs). We invoke a 1D, isothermal, two-fluid formulation to simulate borehole fluid-phase velocity, pressure, volume fraction, and density in oil/water-flow systems. The developed borehole fluid-flow model implements oil-dominant and water-dominant bubbly flow regimes with the inversion point taking place approximately when the oil volume fraction is equal to 0.5. Droplet diameter is dynamically modified to simulate interfacial drag effects, and to effectively account for variations of slip velocity in the borehole. Subsequently, a new successive iterative method interfaces the borehole and formation fluid-flow models by introducing appropriate source terms into the borehole fluid-phase mass-conservation equations. The novel iterative coupling method integrated with the developed borehole fluid-flow model allows dynamic modification of reservoir boundary conditions to accurately simulate transient behavior of borehole crossflow taking place across differentially depleted rock formations. In the case of rapid variations of near-borehole properties, frequent borehole/formation communication inevitably increases the computational time required for fluid-flow simulation. Despite this limitation, in a two-layer reservoir model penetrated by a vertical borehole, the coupling method accurately quantifies a 14% increase of volume-averaged oil-phase relative permeability of the low-pressure layer caused by through-the-borehole cross-communication of differentially depleted layers. Sensitivity analyses indicate that the alteration of near-borehole petrophysical properties primarily depends on formation average pressure, fluid-phase density contrast, and borehole-deviation angle. A practical application of the new coupled fluid-flow model is numerical simulation of borehole production measurements to estimate formation average pressure from two-phase selective-inflow-performance (SIP) analysis. This study suggests that incorporating static (shut-in) PL passes into the SIP analysis could result in misleading estimation of formation average pressure.

Percolation Mathematical Model for Stepped Horizontal Well in Multilayer Fault Block Reservoir

The percolation mechanism and regularity for stepped horizontal well in multi-layer complex fault block reservoir are complex. A percolation mathematical model based on unsteady flow mathematical model is built up in this paper. In the model, the reservoir couples with one horizontal well in sealed reservoir which perforates through mutually unconnected formation. Laplace transform, Stehfest inversion and Conjugate gradient are used to solve the model. The pressure distribution results of different time and production distribution results of different well section can be obtained. The results of pressure drop and pressure drop derivative calculated by this model are close to the results calculated by the Saphir software, and the agreement rate is 99%, which proves the model is of great reliability. Compared with Saphir software, the capacity of horizontal section through multiple sand at the same time can be calculated, which is the advantage of this model. It is not suitable for heterogeneous reservoir and the reservoir with supply boundary, which is the limitation. A two-layer block fault reservoir has been used to carry out the field study through the model, simplifying the irregular shape of reservoir for rectangular reservoir at first. Then a double-stage horizontal well is used to pass through the upper layer and the lower layer orderly in this reservoir, the simulation calculation of the well can use the double-stage horizontal well model, and the model can calculate the average pressure drop and pressure drop derivative of various production phases in the bottom hole accurately .The reservoir flow stage and the flow time in different periods can be judged through pressure drop and pressure drop derivative in the bottom hole, which can also calculate the distribution of production along the horizontal section in different periods at the same time. It can provide theoretical foundation of reservoir research engineering and production engineering design for reservoir development with stepped horizontal well in multilayer complex fault block reservoir.

English

Understanding the behaviour of pressure distribution completed in two layered reservoir subject to both active gas cap and bottom water drive mechanisms is very important in reservoir management. To determine the factors that affect pressure distribution of horizontal wells in a layered reservoir subjected simultaneously with a gas-cap at the top and bottom water drives, well completion was carried out in a particular layer and one of the parameters was varied while the others were kept constant. The results show that the following factors: (i) Wellbore radius (ii) Well Length and (iii) Pay thickness affect pressure distribution in two-layered reservoir subject to both active gas cap and bottom water drive which affect pressure distribution.   Key words: Well, pressure, layer, reservoir, well.

Theoretical Dimensionless Breakthrough Time of a Horizontal Well in a Vertically-Stacked Two-Layered Reservoir System with Varying Architecture Part I: Letter ‘B’ Architecture, Edge Water Drive Mechanism

In this paper, which is Part I of a series, theoretical breakthrough times of different models of a crossflow two-layered reservoir having an architecture similar to letter ‘B’ and experiencing an edge water drive, with or without a top gas, are derived. The theoretical breakthrough times are based on dimensionless pressure distributions of each identified model.

Theoretical Dimensionless Breakthrough Time of a Horizontal Well in a Vertically-Stacked Two-Layered Reservoir System with Varying Architecture Part II: Letter ‘B’ Architecture, Bottom Water Drive Mechanism

When a reservoir experiences water influx, the actual source of the water often cannot be ascertained with precision. Thus well work over measures to minimize the water may not be easy to fashion. Bottom water encroaches through the bottom of the reservoir and rises vertically, appearing in all the wells in the field at the same time, if the wells experience the same production histories. This further makes work over difficult, more so, if there are other external fluid influences akin to a top gas. However, if the arrival time is known, then factors affecting bottom water movement, with or without any other contiguous top gas, may be studied with a view to fashioning an effective work over to mitigate premature water arrival into the well. Horizontal wells are already known to delay encroaching water breakthrough time. For a cross flow layered reservoir completed with a horizontal well in each layer, flow dynamics will certainly be different from a single layer reservoir due to differences in individual layer, layers fluid, wellbore and interface properties and rate histories. In this paper, theoretical expressions for predicting dimensionless breakthrough times of horizontal wells in a two layered reservoir of architecture like letter ‘B’, experiencing bottom water drive mechanism of different patterns, with or without a top gas, are derived. The theoretical breakthrough times are based on dimensionless pressure and dimensionless pressure derivative distributions of each identified model. Twenty-seven (28) different models emerged as the total of the different models possible.

Integration of Well-Test Pressure Data Into Heterogeneous Geological Reservoir Models

Summary This paper presents the application of the ensemble Kalman filter (EnKF) method to the integration of well-test data into heterogeneous reservoir models generated from geological and geophysical data. EnKF does not require computing the gradient of an objective function and, hence, can be applied easily with any reservoir simulator, and more importantly, it is far more efficient than a gradient-based history-matching procedure when the forward model is represented by a reservoir simulator. In the procedure for integrating pressure-transient data considered here, the static geological/geophysical data are assumed to be encapsulated in a multivariate probability-density function (pdf) characterized by a prior mean and covariance for the joint distribution of the porosity and permeability fields. Because the prior mean of the property fields obtained from the core and log data can sometimes be erroneous, a partially doubly stochastic model is applied to account for the uncertainty of the prior mean. In the doubly stochastic model, a correction to the prior mean is adjusted together with the heterogeneous field during history matching. The method is tested with synthetic heterogeneous single-layer and two-layer reservoirs. Excellent data matches are obtained with EnKF in a small fraction of the time that would be required for a gradient-based history-matching process, and the observed data fall within the uncertainty bounds of the ensemble data predictions. In the layered-reservoir case, the uncertainty in rock-property fields is reduced further by integration of production-log data (layer flow rates). We show that problems of statistical inconsistency and poor data matches that are sometimes encountered when matching production data with EnKF do not occur when matching pressure data with the EnKF implementation used here. This undoubtedly occurs because the dynamical system (reservoir-simulator equations) is much more nearly linear for the single-phase-flow problems considered here than for multiphase-flow cases.

Experimental Study on Selective Withdrawal in a Two-Layer Reservoir Using a Temperature-Control Curtain

An experimental study was conducted to investigate the use of a temperature-control curtain in selective withdrawal from a two-layer stratified reservoir. This study focused on the case where cool water at a depth was forced to flow under the curtain. The evolution of the mean flow, the withdrawal water quality, and the mean velocity field were studied using particle image velocimetry and laser-induced fluorescence. Practical relationships were developed for predicting the withdrawal water quality and the interface height as a function of time. The structures of the flow field in both the upper and lower layers are discussed in detail. The flow in the lower layer was dominated by the recirculation eddy induced by the jet flow under the curtain and a relation between the eddy length and the interface height was obtained. Close to the intake, within about 3d (where d=intake diameter), the velocity field can be well described by the potential flow theory. Beyond 3d, however, the flow field considerably deviated from the potential flow theory due to the jet expansion and stratification. A general discussion of the results and engineering applications are also provided.

Pressure Derivative Behavior of Two-Layered Reservoir with Vertical Wells

Layered reservoir systems present a huge challenge to both reservoir and production engineers, because of difficulty encountered in reservoir management and well completions. In this paper, the solution to a 2D reservoir model is utilized to study pressure and pressure derivatives of a two-layered crossflow reservoir with a vertical well. No skin and wellbore effects are included. The interlayer fluid transmissibility ratio is varied for the same layers properties, to study the effects of layers heterogeneity and well completion choice on flow performance. Results show that decreasing values of specific transmissibility ratio, , signifies completion in the more permeable layer, a shift in the pressure response to the left and a short transition period to depletion of the second layer. Furthermore, increasing values  means that the well is completed in the lower permeability layer causing delay in the depletion of the second layer as a result of long transition period.

Nonlinear stability of two-layer non-homogeneous rectangular reservoir with a mixed load

The article deal with stopping issues from the pressure of regularly distributed diametrical forces and pressing on length of axis of two layered anti-gender right angled board. Analyses of accounts shown that taking into account of anti pedigreed affects to the marks of critical parameters 8−10 %.

The Hijiori Hot Dry Rock test site, Japan: Evaluation and optimization of heat extraction from a two-layered reservoir

The Hijiori hot dry rock (HDR) system, Japan, consists of a shallow and a deep reservoir, both in fractured granitic rocks. During a long-term circulation test (LTCT) lasting approximately 18 months and which tested different fluid production scenarios, large changes were observed in output fluid temperatures, pressures, and flow rates. A multi-reservoir, numerical model of the Hijiori HDR system was developed using the finite element heat and mass (FEHM) transfer code and applied to simulations of the LTCT. The model reproduced the pressure, temperature, and flow data observed during the test. Based on the modeling study, it was concluded that most of the produced fluid came from the shallow reservoir, that the permeability of the deep reservoir changed during the initial part of the LTCT, and that the redistribution of injected water between the two reservoirs had little impact on the relative amounts of deep and shallow fluid production. After validating the model on the LTCT, it was used to optimize injection rates in both reservoirs. The model was also used in simulations of reservoir performance where an additional heat transfer surface area has been created in the subsurface through hydraulic fracturing.

Limitations in qualitative and quantitative analysis of time-lapse data due to fluid flow uncertainties

We address some limitations in qualitative and quantitative analysis of time-lapse data due to underlying uncertainties in the flow of reservoir fluids. We explore how seismic signals may evolve over time by developing synthetic time-lapse data based on a variety of flow scenarios including radial flow, multi-phase flow and flows with unstable mobility ratios. Model predictions of water saturation and effective stress are used to construct synthetic impedance profiles. Using an idealized model of water-flood type production we show that qualitative analysis can be limited by the signal complexities resulting from flows in which both water saturation and effective stress change gradually, such as may occur when the injected water and the displaced oil are not separated by a sharp interface. A two-layer reservoir flow model is developed with which the limitations of quantitative analysis are explored. If a quantitative inversion technique is error free the resolution limits and signal noise in the seismic data allow only spatially averaged reservoir properties to be known. In some reservoirs undergoing water flood, volumetrically significant movement of the injected water may occur on length scales below that of the resolution and noise threshold the seismic data allows. In such a reservoir the inversion technique gives good quality information about the average location of the injected water but does not provide information about how all the injected water is moving. Specifically the possibility of thin high permeability layering carrying a significant fraction of the injected water cannot be eliminated. We show that this can introduce great uncertainty in estimates of reservoir performance.